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Mathematics
Mathematics
Problem
Let
y
=
y
(
x
)
y = y(x)
y
=
y
(
x
)
be the solution of the differential equation
(
1
−
x
2
)
d
y
=
[
x
y
+
(
x
3
+
2
)
3
(
1
−
x
2
)
]
d
x
(1 - x^2)dy = [xy + (x^3 + 2)\sqrt{3(1 - x^2)}]dx
(
1
−
x
2
)
d
y
=
[
x
y
+
(
x
3
+
2
)
3
(
1
−
x
2
)
]
d
x
,
−
1
<
x
<
1
-1 < x < 1
−
1
<
x
<
1
,
y
(
0
)
=
0
y(0) = 0
y
(
0
)
=
0
. If
y
(
1
2
)
=
m
n
y\left(\frac{1}{2}\right) = \frac{m}{n}
y
(
2
1
)
=
n
m
,
m
m
m
and
n
n
n
are coprime numbers, then
m
+
n
m + n
m
+
n
is equal to _____.
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